Question

Write the standard form for a parabola that has the following x intercepts: (-4, 0) and (7, 0).

Answer 1

y = x² - 3x - 28

Explanation:

given a parabola with x- intercepts x = a and x = b , then

(x - a) and (x - b) are the corresponding factors and the equation is the product of its factors

y = (x - a)(x - b)

here the x- intercepts are x = - 4 and x = 7 , then the factors are

(x - (- 4)) and (x - 7) , that is (x + 4) and (x - 7) , then

y = (x + 4)(x - 7) ← expand using FOIL , then

y = x² - 3x - 28 ← in standard form